Thermodynamics of ordering and mixing in plagioclase feldspars: atomistic modelling in favour of Landau theory

Abstract

Plagioclase feldspars are key components of terrestrial planets and deriving their phase diagram and activity-composition relations has been the subject of many studies. Three main approaches have been used for thermodynamic modelling of the behaviour of plagioclase feldspars, and all three broadly disagree in terms of the magnitude and relative importance of mixing energies and ordering energies.This study uses Monte-Carlo simulations based on classical atomistic modelling to provide independent constraints over ordering and mixing for anorthite and along its solid solution with albite.Unsurprisingly, Al avoidance plays a key role. The competition between first-neighbour and second-neighbour interactions is highlighted, providing simple explanations to the high degree of short-range order in macroscopically-disordered plagioclase. The mixing properties obtained in this study support strong non-ideality, with negative mixing enthalpy and temperature-dependent mixing entropy. Ordering energies are consistent with studies using Landau theory. Unfortunately the form of the Landau equations hindered parametrisation of a full thermodynamic model from albite to anorthite, even though the thermodynamic formalism remains simple. Reasons, perspectives and implications for the phase diagram of ternary feldspars are discussed.

An anisotropic equation of state for solid solutions, with application to plagioclase

“…Structural and elastic data for plagioclase crystals across the albite-anorthite binary have been collected by Angel et al (1990) and Brown et al (2006Brown et al ( , 2016, and these data are used here to create an anisotropic model for the disordered C 1 (high) plagioclases. Extension to the I 1 space group is left for a future study, given the need to develop an anisotropic Landau-theory consistent with the equation of state (Carpenter, 1988;Dubacq, 2022).…”

Local strain heterogeneity associated with Al/Si ordering in anorthite, CaAl2Si2O8, with implications for thermodynamic mixing behavior and trace element partitioning in plagioclase feldspars

“…A number of different strategies have been adopted to describe the thermodynamic properties of plagioclase feldspars in the context of efforts to produce quantitative descriptions of the stability fields of mineral assemblages under the full range of possible geological conditions. Dubacq (2022) summarised contrasting treatments of mixing properties for the C1 ̅ and I1 ̅ structures at high temperatures as those which smooth out the effects of the discrete C1 ̅  I1 ̅ transition (Ghiorso 1984;Benisek et al 2004Benisek et al , 2010Namur et al 2012;Holland et al 2022), those which treat states with different symmetries as separate solid solutions (Holland and Powell 1992) and those which treat the mixing properties in terms of an Al/Si order/disorder process at anorthite-rich compositions (Carpenter and Ferry 1984;Carpenter 1992Carpenter , 1994). The differences revolve, in effect, around the need (or otherwise) to include a physically correct description of the phase transition approximately half way across the solid solution.…”

“…A significant recent advance in the context of understanding the stability of plagioclase feldspars from an atomic perspective has been provided by a Monte Carlo simulation by Dubacq (2022) which focussed on interactions between nearest neighbour and next nearest neighbour tetrahedral cations. This author concluded that superposition of I1 ̅ ordering on a C1 ̅ solid solution, with large ordering energies for anorthite, can provide reliable results in terms of energy and ordering across the solid solution.…”